The application of rf excitation to a sample and the pick up of resulting resonant signal is accomplished in a structure surrounding the sample which may be a helical coil, saddle coil, resonant cavity, or a bird cage resonator. The latter structure is the object of the present work, wherein it is desired to couple to a sample which is substantially ellptical in cross section. A bird cage coil is a ladder circuit which closes on itself wherein the current flow around the coil is distributed sinusoidally. As a tuned rf circuit, it is employed in nuclear magnetic resonance apparatus for either or both of the functions of rf excitation and signal detection.
The bird cage coil differs in essential matter from saddle coils, helices and likegeometries by its discrete structure. For the bird cage coil, it is required that the phase shift be discretely distributed around the circumference of the coil from zero to 2.pi. (or 2.pi.k where k is an integer). The phase shift of each element is quite frequency dependent and as a consequence, the bird cage coil is tuned at a discrete frequency to achieve the desired phase shift constraint.
The bird cage coil is particularly well suited to large volume samples as are routinely encountered with apparatus for medical imaging and in vivo analytic spectroscopy. Prior art birdcage coils are discussed by Hayes et al, J. Mag. Res., vol. 63, pp. 622-628 (1985).
The bird cage structure may be regarded as a periodic structure which closes on itself. Periodic elements of the structure produce phase shifts which must aggregate to some multiple of 2.pi. when summed over the closed loop. Geometrically, the resonator has cylindrical symmetry and it is desired that the rf current in the axial direction along the periphery of the structure be proportional to sin k.theta. and/or cos k.theta. where .theta. is the azimuthal angle about the cylindrical axis. The mode k=1 produces the most uniform transverse magnetic fields, such as are commonly used in analytic NMR applications.
The imperfect coupling component between an object studied and the NMR transmitter/receiver limits the performance of the measurement in several ways. First, there is the limitation in the sensitivity of instrumental performance as the weak resonance signals are not coupled in to the receiver in degree sufficient to exceed the inherent noise. There is the limitation on signal to noise ratio which is a consequence of a non-optimum filling factor, e.g., where the object occupies less than the entire sensitive volume. There is also a loss in precision due to the inhomogeneity with which the rf magnetic field is distributed throughout the sensitive volume.
The coupling component takes the form of an inductive structure surrounding the object under study. Typically this may assume the form of a cavity (for extreme frequencies), or more commonly, solenoidal, saddle or birdcage geometry. The birdcage geometry is the subject of the present work wherein it is desired to utilize a birdcage geometry in elliptical cross section to better match the cross section of the human body for medical imaging purposes.
RF coils of elliptic birdcage cross section are known for use in medical imaging of the human head and body. See reported work by Binson, Martin, Griffiths and Edwards, Proc. SMRM, p.272 (1992); Li and Smith, Proc. SMRM, 1342 (1993); Kurczewski, Pavlovich, Stiedly and Rollins, Proc. SMRM, p. 4025 (1992); Li, et al, Proc. ISMRM, p.1411 (1996).
The Binson, et al work taught an arrangement of leg elements such that segments formed by the coil elements and the central axis of the elliptical cylinder (in the cross section thereof) comprise equal areas, the current being distributed among the several legs sinusoidally about the end rings of the coil.
Li and Smith studied the B.sub.1 field obtainable from an elliptical coil having 16 elements (legs) equally spaced in perimeter distance increments on the periphery. For an ellipse of semi-major axis A and semi-minor axis B their approximate formula for the current density on the surface of the ellipse is given as EQU J.sub.c (.theta.)=J.sub.0 cos(.theta.)/(B.sup.2 cos.sup.2 (.theta.)+A.sup.2 sin.sup.2)
to produce a magnetic field substantially parallel to the minor axis.
Kurczewski, et al constructed an elliptic birdcage coil with legs spaced at equal angular increments.
The starting point for the present work is to obtain the continuous surface current distribution K.sub.z (.theta.) on the surface of an elliptical cylinder, which current distribution will produce uniform and orthogonal magnetic fields for quadrature operation in the interior of the ellipsoid. The well known technique of conformal mapping can be employed to transform to the simpler case of cylindrical geometry. Next, a discrete current distribution is obtained, which yields the equivalent field distribution as for the continuous current case. The discrete currents are preferably supported on 4M legs (M, an integer) in order to effectuate quadrature operation. The discrete case is further constrained to the situation of equal peak amplitudes driving the orthogonal modes in order that passive quadrature hybrid combiners may be employed to produce equal power splitting between ports. By reciprocity, the analysis for excitation of the birdcage coil from an rf current source is essentially duplicated for the reception of signals induced on the coil from a sample within the coil. Throughout this work, the sample excitation function for the coil is understood to describe the parallel signal reception function.
In the present work, discrete legs are spaced unequally in the geometric sense on the elliptical perimeter and at equal angular intervals of electrical phase.